Good art and a good plot anf you have a manga i want to read, if the story is bad i refuse to read ot but if the characters are bad it just makes the story drop in quality :/
So both good art and plot ^^

I buy my manga almost exclusively from used book stores, so here are my criteria:

5th most important - The art. Some manga art just doesn't sit well with me.
4th most important - The publisher. I'm not a Jump fan. Stories are too childish sometimes.
3rd most important - The author/artist. If it's a toss up between two books, the author I like better will usually win.
2nd most imortant - The Story. I will almost always read a story if the description on the back grabs me.
1st most important - First issue. I refuse to read a manga where I can't start with issue number one. No matter if it gets approval from the rest of my criteria - No first issue, no sale.

I think the first thing when I see a manga I see the art, so I guess that would be my first attraction towards a manga.
The second would be to see if it has romance lol. I like action manga's that have subtle romance. I think after reading so many shoujo manga's I've pretty much have covered that section and I can assume what will happen in the storyline and who will end up with who. In an action manga, you never know hehe.
The last would be the storyline. I give it about the first ten chapters if I would like to continue or not.

Being somebody who does not actively look for manga all the time it is hard for me to say. New manga series do not get the same hype a new anime series would . But I guess I only check out mangas if I've finished the anime (in Bleach and Fairy Tails case) or if its an increasingly popular manga that has yet to get an anime (In assassination classrooms case)

characters. Characters. Characters
Seriously, you can have the most plain story but if you have really interesting/well-written characters, they're bound to naturally arise to intriguing circumstances or shed new lights on seemingly understood phenomenons/truths. Or if you can also squeeze in a solid plot, man I will read the shit out of it. Still, I guess unusual circumstances make a good part of the excitement so a story comes second but can also sometimes make up for the characters not being exactly fleshed out(SnK). Aesthetics next I suppose because I can't read anything when I'm distracted by an artist who looked like they never even practiced. If we're talking purely first glance though, I look at the genres, art, then summary.

In all honesty what attracts me to manga is being able to finish stories and being able to progress through a series faster because I can read faster than I can watch an anime episode of that manga. I used to prefer anime over manga but after getting tired of watching some filler I decided to read that part instead and I ended up finishing the series.

mainly story i think. i've noticed i like romance and comedy much more in manga then most other things. it does bother me a little if the drawings aren't that great but if a story is good enough i can over look it